What will be the quotient when 2143 is divided by 38?

Introduction / Context:
This question tests your ability to perform integer division with multi digit numbers. You are asked to find the quotient when 2143 is divided by 38. The focus is on accurate multiplication and subtraction rather than any advanced concept. Such questions are common in aptitude tests to check mental arithmetic and basic numerical handling skills.

Given Data / Assumptions:

- Dividend = 2143. - Divisor = 38. - We are interested only in the quotient, not the remainder.

Concept / Approach:
We want to know how many whole times the number 38 fits into 2143. A practical way is to estimate around convenient multiples of the divisor. We first try a rough multiple such as 50 times 38 and then adjust up or down, checking nearby multiples until we find the largest multiple of 38 that does not exceed 2143. The corresponding factor is the quotient, and the leftover part is the remainder. Although the remainder is not required, it can help verify that we chose the correct multiple.

Step-by-Step Solution:
Step 1: Start by estimating 38 * 50, because 50 is a convenient round number. Step 2: Compute 38 * 50 = 1900. Step 3: Compare 1900 with 2143. The difference is 2143 - 1900 = 243, so we can still multiply 38 by a few more units. Step 4: Try adding 6 more multiples of 38. Compute 38 * 6 = 228. Step 5: Add this to 1900: 1900 + 228 = 2128. Step 6: Now compare 2128 with 2143. The difference is 2143 - 2128 = 15. We cannot add another full 38 because 2128 + 38 = 2166, which would exceed 2143. Step 7: Therefore, the largest multiple of 38 that is less than or equal to 2143 is 38 * 56 = 2128. Step 8: The quotient is 56 and the remainder is 15, though only the quotient is required.

Verification / Alternative check:
We can verify the quotient by performing the division 2143 ÷ 38 in the standard long division format. Repeated subtraction of 38 or stepwise division will also show that after 56 groups of 38, there is a leftover of 15, and that any attempt to take a 57th group of 38 would exceed 2143. Another quick sanity check is to approximate: 2143 ÷ 40 is a little over 53, so a quotient around 54 to 56 is reasonable. The more precise calculation confirms that 56 is correct.

Why Other Options Are Wrong:
If the quotient were 55, the product 38 * 55 would be 2090, leaving a remainder of 53; while this is less than 2143, it is not the largest possible quotient because 56 still fits. A quotient of 57 would give 38 * 57 = 2166, which is greater than 2143 and therefore impossible. Similarly, 54 is too small because we already know 56 is achievable. Thus, only 56 is both valid and maximal.

Common Pitfalls:
Students sometimes stop at 50 because 1900 feels close enough, or they miscalculate products like 38 * 6 or 38 * 7, leading to wrong conclusions. Others may confuse the remainder with the quotient. Carefully calculating nearby multiples and explicitly comparing them with the dividend helps avoid these mistakes.

Final Answer:
The quotient when 2143 is divided by 38 is 56, which corresponds to option A.